A123924 Numbers k such that 2^(k+1) + 3^k is prime.

0, 1, 2, 3, 4, 5, 6, 9, 11, 12, 15, 17, 22, 32, 33, 35, 36, 46, 47, 59, 63, 80, 101, 154, 159, 173, 221, 225, 236, 250, 281, 347, 789, 992, 1607, 1631, 1983, 2072, 3616, 3702, 5076, 5957, 6335, 8771, 10203, 10984, 12203, 12350, 13660, 14891

Offset: 1

Author

Alexander Adamchuk, Nov 20 2006

Keywords

• nonn

Comments

Also numbers k such that A123601(k) = A085279(k+1) = 2^(k+1) + 3^k. There are only 4 known primes of form the 2^k + 3^k, {2, 5, 13, 97} = A082101, corresponding to k = {0, 1, 2, 4}.

Crossrefs

Cf. A082101 (primes of form 2^k + 3^k), A085279, A123601 (smallest prime of the form p^n + q^n + r^n, where p,q,r are primes).

Programs

Mathematica

Do[f=2^(n+1)+3^n;If[PrimeQ[f],Print[{n,f}]],{n,0,347}]
Select[Range[0,6400],PrimeQ[2^(#+1)+3^#]&] (* Harvey P. Dale, Mar 04 2019 *)

PARI

is(n)=ispseudoprime(2^(n+1)+3^n) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

More terms from Stefan Steinerberger, May 12 2007

a(44) from Jinyuan Wang, Aug 02 2021

a(45)-a(50) from Michael S. Branicky, Aug 05 2021